Solve sin^{2}30^circ+cos^245^circ+cos^260

$$\sin ^ { 2 } 30 ^ { \circ } + \cos ^ { 2 } 45 ^ { \circ } + \cos ^ { 2 } 60$$

Evaluate

$$1$$

Solution Steps

Get the value of \sin(30) from trigonometric values table.

$$\left(\frac{1}{2}\right)^{2}+\left(\cos(45)\right)^{2}+\left(\cos(60)\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}+\left(\cos(45)\right)^{2}+\left(\cos(60)\right)^{2}$$

Get the value of \cos(45) from trigonometric values table.

$$\frac{1}{4}+\left(\frac{\sqrt{2}}{2}\right)^{2}+\left(\cos(60)\right)^{2}$$

To raise \frac{\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\left(\cos(60)\right)^{2}$$

Get the value of \cos(60) from trigonometric values table.

$$\frac{1}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\left(\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+\frac{1}{4}$$

Add \frac{1}{4} and \frac{1}{4} to get \frac{1}{2}.

$$\frac{1}{2}+\frac{\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1}{2}+\frac{2}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{2}+\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+\frac{1}{2}$$

Add \frac{1}{2} and \frac{1}{2} to get 1.

$$1$$